Question

control systems

1) Using Routh Hurwitz Stability Criteria, determine whether the following system of equation is stable or not. a) S4+253+3S2+45+5=0 2) Using the Routh Hurwitz stability criterion, determine the range of K for stability of the following characteristic equation. a) s4+2s8+(4+K)s2+9s+25=0 3)Sketch the root-locus of the following systems a) G(s)H(s) = s(s+1)(s+2) b) G(s)H(s) = 52(8+3.6) K(5+1)

Answer 1

Giver over 54+953+38+45+5=0 Routh Array st ll 35 Nord sêgn changes in Ist column of Routh Array is =2 a No.66 Poles on Right halt ot soplane a Given system is unstable) Given S 3 +as+l Akls +95 +2520 Routh Array S4 11 (4+1) 25 ka 4+4-02 ů s § 2 (448)-9 ak, as Taking kike Fu 4 - solas

For the Systen tobe stable All the coefficients in Ist column are of same sign is, the - ki= 4+k-9 2 so & k2 a 9. so so ki 24+4-aaso aj k > Sot ark > 6.055) 2) Giver system will be stable for kobioss)